Hausdorff良紧空间是超紧的充要条件

Necessary and Sufficient Conditions for Hausdorff N-compact Space to Be Ultracompact

中文摘要:

      本文给出L—Fuzzy Hausdorff良紧空间是赶紧的充要条件.在此基础上,讨论了使Hausdorff空间的四种紧性等价的条件。另外,我们还研究了分子网的格代数特征与空间层次结构的关系.

英文摘要:

      The main results of this paper are as follow.Theorem 5 A Hausdorff N-compact space (L^X , δ) is ultracompact if and only if its (L^X , δ_f) is a weakly induced space or strong Hausdouff space.Theorem 7 Let (L^X , δ) be a Hausdorff space. Then its F-compactness, strong F-compactness, N-compactness and ultracompactness are equivalent to each other if and only if (L^X , δ_f) is a weakly induced space or strong Hausdorff space.